There is a need for better image rejection filters to be used in wireless systems. In general, an image rejection filter is implemented as a bandpass filter that passes only positive frequencies. Since the magnitude of the transfer function is not symmetric about DC, the transfer function is complex. FIG. 1 is a diagram illustrating a low pass to bandpass filter transformation. Since the filter shown requires complex signals, it needs to be implemented as a filter with two real inputs. FIG. 2 is a block diagram illustrating an implementation of such a complex filter. Input 202 is referred to as the in phase or I input and input 204 is referred to as the quadrature or Q input. As shown in FIG. 2, the I channel and the Q channels are linked. An output QO of the Q channel 214 is fed into a second input I2 to the I channel 206. Likewise, an output IO of the I channel 212 is fed into a second input Q2 to the Q channel 208.
Ideally, to implement a complex filter as shown in FIG. 2 it would be useful to have a filter that has a minimum number of op amps or other active components. “CMOS Mixers and Polyphase Filters for Large Image Rejection” by Farbod Behbahani, Yoji Kishigami, John Leete, and Asad A. Abidi, published in the IEEE Journal of Solid-State Circuits, Vol. 36, No. 6, June 2001, page 873 and 878 describes a polyphase multiple pole filter that includes several RC stages. The design is useful, but it is difficult to implement desired types of bandpass filters and the multiple stages attenuate the signal so that amplification of the output is required. “An Image-Rejecting Mixer and Vector Filter with 55-dB Image Rejection over Process, Temperature, and Transistor Mismatch,” Thomas Hornak, Knud L. Knudsen, Anderew Z. Grezegorek, Ken A. Nishimura, and William J. McFarland, IEEE Journal of Solid-State Circuits, Vol. 36, No. 1, January 2001, page 23 and 26 describes an image rejection filter that integrates op amps into the filter design so that amplification is built into the filter. This design also has the advantage that desired types of bandpass filter responses can be implemented. However, the illustrated design only provides one pole per op amp. A complex multiple pole filter therefore would require an op amp for each pole in each channel. It would be desirable if a filter could be designed that could be used in an image rejection system and would use fewer op amps per pole. Such a filter could use less power and take up less space on a chip than currently available designs.